Towards the experimental clarification of quarkonium polarization

Abstract: We highlight issues which are often underestimated in the experimental analyses on quarkonium polarization: the relation between the parameters of the angular distributions and the angular momentum composition of the quarkonium, the importance of the choice of the reference frame, the interplay between observed decay and production kinematics, and the consequent influence of the experimental acceptance on the comparison between experimental measurements and theoretical calculations. Given the puzzles raised by the available experimental results, new measurements must provide more detailed information, such that physical conclusions can be derived without relying on model-dependent assumptions. We describe a frame-invariant formalism which minimizes the dependence of the measurements on the experimental acceptance, facilitates the comparison with theoretical calculations, and probes systematic effects due to experimental biases. This formalism is a direct and generic consequence of the rotational invariance of the dilepton decay distribution and is independent of any assumptions specific to particular models of quarkonium production. The use of this improved approach, which exploits the intrinsic multidimensionality of the problem, will significantly contribute to a faster progress in our understanding of quarkonium production, especially if adopted as a common analysis framework by the LHC experiments, which will soon perform analyses of quarkonium polarization in proton-proton collisions.

Towards the Experimental Clarification of Quarkonium Polarization

This paper delves into the nuances of quarkonium polarization and aims to illuminate some oft-overlooked issues in experimental analyses. Quarkonium physics, particularly its polarization, plays a pivotal role in refining our understanding of Quantum Chromodynamics (QCD). Despite a wealth of experimental data spanning decades, understanding remains murky, marred by inconsistencies and contradictions in certain findings.

The authors underscore several experimental challenges in quarkonium polarization analyses. They argue that parameters from angular distributions are often neglected, highlighting the necessity of understanding the angular momentum composition of quarkonium, the importance of the reference frame choice, and the interplay between observed decay and production kinematics. They propose a frame-invariant formalism to minimize experimental biases, offering a more comprehensive understanding of quarkonium production mechanisms.

Experimental Insights and Challenges

Key experiments, such as those performed at the Tevatron, have shown that differential cross-sections largely exceed expectations derived from leading-order Color Singlet Model calculations. Subsequently, the non-relativistic QCD (NRQCD) framework has provided a partial understanding, though heavily reliant on adjustable non-perturbative parameters, reducing the impact of its predictive capabilities.

Moreover, theoretical models diverge significantly in their predictions of quarkonium polarization. NRQCD calculations predict transversely polarized states at high $p_T$, whereas newer NLO calculations suggest strong longitudinal polarization components. This theoretical divergence offers a prime opportunity for experimental discrimination, yet current findings are ambiguous due to large experimental uncertainties and a significant portion of indirect J/ψ production from feed-down processes.

Such findings underscore the immense complexity of polarization measurements. Several experiments show contradictory results, further muddled by the lack of continuity between fixed-target and collider results.

Proposals for Improved Measurements

This paper advocates for several strategies to enhance data accuracy and interpretation:

• Comprehensive Data Collection: Emphasizing the necessity of measuring the full dilepton decay angular distribution, rather than solely relying on basic polar anisotropy metrics.

• Multiple Reference Frames: Conducting analysis in different polarization frames to prevent extrinsic dependencies on experimental kinematics and acceptance.

• Narrow Kinematic Cells: Benefits of reporting results in narrow rapidity and transverse momentum bins to minimize distortion through acceptance corrections.

• Frame-Invariant Quantities: Introduction of frame-independent angular parameters to counteract systematic biases and ensure robust cross-experimental comparisons.

The authors highlight that quarkonium polarization analyses must transcend simplistic, single-frame polar measurements. They posit that the expansion into full angular distribution analytics, involving multiple frames, will provide a richer understanding of quarkonium's angular momentum properties and the dynamics of its production mechanisms.

Implications and Future Directions

The proposed methodologies call for an overhaul of experimental conventions and pave the way for improved theoretical models better aligned with experimental capabilities. The frame-invariant approach, in particular, offers a promising tool for self-consistency checks within experimental setups. These strategies collectively aim to unravel the complexities surrounding quarkonium polarization, potentially propelling advancements in AI for data processing and statistical analysis within these experimental contexts.

In conclusion, adopting these comprehensive analytical frameworks could catalyze a significant leap forward in our comprehension of quarkonium polarization, facilitating deeper insights into the fundamental principles of QCD and enhancing data integrity for future experimental endeavors at high-energy colliders like the LHC.